Mathematical Sciences: Topics in Ergodic Theory and Analysis

贝娄将研究几乎所有的收敛分析和遍历理论。她将研究关于绝对可积函数的几乎处处收敛的问题，实线上的中心极限定理及其向遍历设置的转移，以及与Hopf老问题的解有关的问题。奇异积分技术将得到进一步的发展和应用。这个项目涉及遍历理论的研究。遍历理论一般关注理解系统的平均行为，其动力学过于复杂或混乱，无法在微观细节上进行跟踪。在“动力学”的标题下，可以放置关于抽象变换如何作用于光滑空间的现代理论。通过这种方式，遍历理论在寻求对均匀空间上的流动进行分类时与几何联系在一起。

Bellow will study almost everywhere convergence in analysis and ergodic theory. She will investigate questions concerning almost everywhere convergence for absolutely integrable functions, the central limit theorem on the real line and its transference to the ergodic setting, and questions related to the solution of an old problem of Hopf. Singular integral techniques will be further developed and applied. This project involves research in ergodic theory. Ergodic theory in general concerns understanding the average behavior of systems whose dynamics is too complicated or chaotic to be followed in microscopic detail. Under the heading "dynamics can be placed the modern theory of how groups of abstract transformations act on smooth spaces. In this way ergodic theory makes contact with geometry in its quest to classify flows on homogeneous spaces.